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I'm taking a combinatorics course, and I was trying to practice from a book I took from the library. unfortunately there are no answers in this book, and there was a question I didn't know even how to approach to. I'd really appreciate it if anyone could give me an advice on how to think about it:

Given the group $\{1, 2, \ldots, n\}$, choose $r$ different numbers so that no two are sequential. e.g for $r = 3$ and $n>r$, $\{1,3,5\}$ is a valid group but $\{1,4,5\}$ isn't valid.

Thank you very much for your time and attention!

Matti P.
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E. Ginzburg
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    Please refer: https://math.stackexchange.com/questions/1030145/combinatorics-question-about-choosing-non-consecutive-integers and https://math.stackexchange.com/questions/490405/choosing-numbers-without-consecutive-numbers – Prakash Nov 08 '19 at 08:23
  • what is it asking for? express the number of valid groups in terms of n and r? – Y.T. Nov 08 '19 at 08:28
  • thank you very much. I'm sorry, I've tried looking for similar problems, but haven't encountered those posts. – E. Ginzburg Nov 08 '19 at 19:14

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